¡Más allá de los números! La exploración fenomenológica de la geometría y el espacio

Luis Alberto Canela Morales

doi:10.23925/2764-0892.2022.v2.n1.e62698

Authors

Luis Alberto Canela Morales El Colegio de Veracruz https://orcid.org/0000-0002-3740-5234

DOI:

https://doi.org/10.23925/2764-0892.2022.v2.n1.e62698

Keywords:

Phenomenology, Geometry, Non-Euclidian Geometry, Arithmetics, Spatiality

Abstract

The phenomenological proposal of Husserl, although initiated with a study on the nature of number and mathematical functions, encompasses much more than that. A series of posthumously edited essays, spanning the years 1890-1908, are known, focusing on understanding the advancements in (Euclidean and non-Euclidean) geometry and its role in the constitution of physical space. Studies on Euclidean and non-Euclidean geometry would continue the investigation of Philosophy of Arithmetic, as both share the Grundgedanken, that is, the set of tools and topics revolving around the notion of symbolic representation. The objective of this article is to present, in a general manner, the main problems Husserl faces concerning geometric and spatial themes. It will attempt to reconstruct, in a historical-critical way, essential aspects of the topics and issues in the philosophy of geometry as Husserl develops it in his early phenomenological works.

References

A) Tomos de Husserliana

[Hua XII] Philosophie der Arithmetik. Mit ergänzenden Texten (1890-1901). Hrsg. von Lothar Eley. 1970.

[Husserliana XX/1] Logische Untersuchungen. Ergänzungsband. Erster Teil. Entwürfe zur Umarbeitung der VI. Untersuchung und zur Vorrede für die Neuauflage der Logischen Untersuchungen (Sommer 1913). Hrsg. Ulrich Melle. The Hague, Kluwer Academic Publishers, 2002

[Hua XXI] Studien zur Arithmetik und Geometrie. Texte aus dem Nachlass (1886-1901). Hrsg. von Ingeborg Strohmeyer. 1983.

[Hua XXII] Aufsätze und Rezensionen (1890-1910). Hrsg. Bernhard Rang, The Hague, Martinus Nijhoff, 1979.

B) Husserliana Dokumente

Husserl, Edmund (1994). Briefwechsel. Hrgs. Karl Schuhmann In Verbindung mit Elisabeth Schuhmann. The Hague, Kluwer Academic Publishers.

Band I: Die Brentanoschule

Band V: Die Neukantianer.

C) Bibliografía

Alves, P. (2010), Fenomenología del tiempo y de la percepción, Biblioteca Nueva, Madrid. Trad. Francisco Conde Soto.

Aranda, V. (2021) Completeness: From Husserl to Carnap, Log. Univers. 16, 57–83. https://doi.org/10.1007/s11787-021-00283-4

Boi, L. (2004) Questions Regarding Husserlian Geometry and Phenomenology. A Study of the Concept of Manifold and Spatial Perception, Husserl Studies 20, pp. 207–267.

Canela Morales, L. A. (2013) El concepto fenomenológico de cinestesia y la correlación con las secuencias del campo visual: un análisis a las lecciones de Cosa y espacio de 1907. Eikasia. Revista de Filosofía, 47, pp. 751-776.

Canela Morales, L. A. (2014) De las cinestesias oculomotoras al espacio objetivo: la constitución del espacio tridimensional, Stoa, 5 (9), pp. 5-18.

Canela Morales, L. A. (2023) Ser y calcular. El problema de las entidades matemáticas en la fenomenología temprana de Edmund Husserl, Editorial Aula de Humanidades, Bogotá, Colombia.

Claesges, U. (1964), Edmund Husserls theorie der Raumkonstitution, The Hague, Martinus Nijhoft.

da Silva, J. (2012) Husserl on Geometry and Spatial Representation, Axiomathes 22:5–30.

Fernández Beites, P. (1999), Fenomenología del ser espacial, Publicaciones Universidad Pontificia Salamanca, Salamanca.

García-Baró, M. (2008), Teoría fenomenológica de la verdad. Comentario continuo a la primera edición de Investigaciones lógicas de Edmund Husserl, Publicaciones de la Universidad Pontifica de Comillas, Madrid.

Giorello, G. y C. Sinigaglia (2007), “Space and Movement. On Husserl’s Geometry of the Visual Field”, en Luciano Boi, et. al (Ed.), Rediscovering Phenomenology. Phenomenological Essays on Mathematical Beings, Physical Reality, Perception and Consciousness, Springer, Dordrecht, The Netherlands.

González Porta, M. A. (1999) Los orígenes de la virada antipsicologista en Husserl (La reseña a Schroeder de 1891 revisada). Thémata Revista de Filosofia, v. 21, p. 85-116.

González Porta, M. A. (2007) Un análisis del opúsculo de Kasimir Twardowsky ‘Inhalt und Gegenstand’ en la perspectiva de su significación para la escuela de Brentano”, Síntese., 34, nº. 109, 261-282.

González Porta, M. A. (2020) Brentano and his school on the psychological method, Brentano Studien, 17, p. 35-66.

Haaparanta, L. (1996) The model of geometry in logic and phenomenology, Philosophia Scientiæ, tomo 1 (2), p. 1-14

Hartimo, M. (2008) From geometry to phenomenology, Synthese, 162:225–233. DOI 10.1007/s11229-007-9177-6

Husserl, E. (1999) Investigaciones lógicas. Trad. José Gaos y Manuel García Morente, Alianza, Madrid.

Keiichi, N. (1993) Husserl and the Foundations of Geometry. En Philip Blosser, et. al. Contributions to phenomenology. Japanese and Wester phenomenology, Kluwer Academic Publisher, Dordrecht/Boston/London.

Lobo, C. (2021) The limits of the mathematization of the living and the idea of formal morphology of the living world following Husserlian phenomenology, Theory in Biosciences. https://doi.org/10.1007/s12064-021-00348-4

Rosado Haddock, G. (2012) Husserl’s Conception of Physical Theories and Physical Geometry in the Time of the Prolegomena: A Comparison with Duhem’s and Poincare´’s Views, Axiomathes (22):171–193. DOI 10.1007/s10516-011-9165-9

Ströker, Elizabeth (1987), Investigation on in philosophy of Space, Athens, Ohio University Press, OH. Trad. Algis Michunas.

Stumpf, C. (1873), Über den psychologischen Ursprung der Raumvorstellung, Verlag von S. Hirzel, Lepzig.